The only way you can even stretch Management skill into 'lowering prodcution cost' is that if/when NPC wages are re-enabled... especially on larger ships or other things with long prod times... you may save a bit in wages in that each item that takes a month shorted prod time will have a month's fewer NPC wages tied into the cost, or that same months worth of NPC wages will aloow for more product.

Likely insignificant for items or other things with small prod times and small NPc demands.... but for the larger cap ships.... it can start to come into play as a factor.. though admittedly a very minor one compared to the other costs of building those ships (prod cost, RM costs, station costs)